Psychology 513 Advanced Research Methods

1
Psychology 513Advanced Research Methods

• Cumming and Finch (2001)
• Primer on Confidence Intervals

2
Why Use Confidence Intervals?

• Gives point and interval information
• Direct link to NHST
• Does CI include zero?
• Supports meta-analytic thinking
• Estimation rather than accept/reject
• Information about precision
• Width of CI

3
Overview

• Confidence intervals for mean(s)
• Confidence intervals for effect sizes
• What is an effect size?
• Cohens d perhaps the most common effect size
  measure for comparing means

4
Aims

• Case 1 Single group design (one-sample t-test)
• Case 2 Two independent groups (independent
  measures t-test)
• Case 3 Two repeated measures (repeated measures
  t-test)

5
Confidence Intervals for Mean(s)

• Case 1 mean of a single group
• Xbar (t)(SE)
• Case 2 two independent groups
• (Xbar1 Xbar2) (t)(SE)
• Case 3 repeated measure
• Dbar (t)(SE)

6
Noncentral Distributions

• Consider the case of the one-sample t
• We know the distribution of t under the null
• We dont know the distribution of t if the null
  is false estimate what it would be
• CI for effect size will be based on a noncentral
  distribution

7
Hypothesis Testing

• Use central distribution because we assume the
  null is true
• p-value tells us the probability of getting a
  value this extreme, given that the null is true

8
CIs for m vs. CIs for d

• How do you decide which to compute?
• Depends on what you want to know
• Original units or standardized effect size
• May help foster meta-analytic thinking